[2009-04-11] Sphericon dice
A sphericon is a right bicone with one side (that is, one half of the bicone cut along a plane containing the axis of rotation) rotated 90 degrees relative to the other. The resulting solid is oloid-like. The derivation from a bicone suggested to me, by analogy, the possibility of polyhedral dice based on the sphericon just as common d10s are based on the bicone. (See my alphabet dice page for an application of biconal/bipyramidal dice.) Basically, the idea is to use faceted sphericons for dice instead of faceted bicones. The movie shows a 16-sided faceted sphericon, which, if the faces were numbered, would be a fair 16-sided die. The number of sides must be a multiple of eight; otherwise, there will be certain positions in which the die will rest with an edge rather than a face in the vertical position.
Update: Turns out this does not, in fact, work. At least not nearly as simply as I first imagined. In the 16-sided sphericon die shown above, there are two kinds of faces: Those that are adjacent to the plane along which the two halves of the bipyramid have been split and rejoined (colored red), and those which are not adjacent to that plane (colored blue). Such a die resting on a red face will present another red face "up" and parallel to the plane of the ground or table, but if resting on a blue face, it will present an edge between red and blue faces in the "up" position. This makes it very difficult to read, and while it might be possible to contrive some arrangement, analogous to a tetrahedral four-sided die, in which a 16-sided sphericon is read based on which face is "down," it's hard to imagine how it could be made easily readable. Perhaps a hollow, transparent shell with the numbers printed on the inside? In any case, such an arrangement is unlikely to be nearly as satisfying as I originally imagined.
last modified 2010-10-19